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VA Il’in (1999)
A Wave Equation with a Bounded Control on Two Ends for an Arbitrary Time IntervalDiffer. Uravn., 35
(1999)
The Wave Equation with a Boundary Control at One End and the Other End Fixed, Differ
(2009)
Longitudinal Vibrations of a Rod Consisting of Two Segments of Different Densities and Elasticities in the Case of Identical Wave Travel Time on Each Segment
(2011)
Boundary Control by an Elastic Force at One End of a Nonhomogeneous Rod and the Other End Free for the Passage of a Wave through Each of the Nonhomogeneous Parts at the Same Time
AV Belikov (2010)
Boundary Control by Displacement at One End of a Nonhomogeneous Rod with the Other End Fixed in the Case of Coinciding Times for the Passage of a Wave through Each of the Inhomogeneity PartsDiffer. Uravn., 46
(2011)
An Optimization Scheme for Boundary Control by Displacement at Two Ends of the Oscillations of a Rod Consisting of Two Different Segments
We study a boundary displacement control at two ends of an inhomogeneous rod that has two parts of distinct densities and elasticities in the case of coinciding wave propagation times over these parts. The control acts on a time interval of critical length. We obtain a closed analytical form of the boundary displacement control bringing the rod in critical time from the initial state of rest into a given terminal state specified by given terminal displacement and terminal velocity.
Differential Equations – Springer Journals
Published: Dec 17, 2013
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